Question

In a triangle abc if ad is the median show that ab2+ac2=2(ad2+bd2)

Answer 1

Step-by-step explanation:

Given:ABC is a triangle, in which AD is a median on BC.

construction :- draw a line AM perpendicular to BC.

to prove : AB² + AC² = 2(AD² + BD²)

proof :- when , it means AD is perpendicular on BC and both angles are right angle e.g., 90°

then, from ∆ADB,

according to Pythagoras theorem,

AB² = AD² + BD² ..... (1)

from ∆ADC ,

according to Pythagoras theorem,

AC² = AD² + DC² ...... (2)

AD is median.

so, BD = DC .......(3)

from equations (1) , (2) and (3),

AB² + AC² = AD² + AD² + BD² + BD²

AB² + AC² = 2(AD² + BD²)

[hence proved ]